Algebra

A Graduate Course

I. Martin Isaacs (Autor)

Buch | Softcover

516 Seiten

1994
American Mathematical Society (Verlag)
978-1-4704-8450-7 (ISBN)

Infos

This book, based on a first-year graduate course the author taught at the University of Wisconsin, contains more than enough material for a two-semester graduate-level abstract algebra course, including groups, rings and modules, fields and Galois theory, an introduction to algebraic number theory, and the rudiments of algebraic geometry. In addition, there are some more specialized topics not usually covered in such a course. These include transfer and character theory of finite groups, modules over artinian rings, modules over Dedekind domains, and transcendental field extensions. This book could be used for self study as well as for a course text, and so full details of almost all proofs are included, with nothing being relegated to the chapter-end problems. There are, however, hundreds of problems, many being far from trivial. The book attempts to capture some of the informality of the classroom, as well as the excitement the author felt when taking the corresponding course as a student.

Autor

I. Martin Isaacs, University of Wisconsin, Madison, WI.

Inhalt

Part One. Noncommutative algebra
Chapter 1. Definitions and examples of groups
Chapter 2. Subgroups and cosets
Chapter 3. Homomorphisms
Chapter 4. Group actions
Chapter 5. The Sylow theorems and $p$-groups
Chapter 6. Permutation groups
Chapter 7. New groups from old
Chapter 8. Solvable and nilpotent groups
Chapter 9. Transfer
Chapter 10. Operator groups and unique decompositions
Chapter 11. Module theory without rings
Chapter 12. Rings, ideals, and modules
Chapter 13. Simple modules and primitive rings
Chapter 14. Artinian rings and projective modules
Chapter 15. An introduction to character theory
Part Two. Commutative algebra
Chapter 16. Polynomial rings, PIDs, and UFDs
Chapter 17. Field extensions
Chapter 18. Galois theory
Chapter 19. Separability and inseparability
Chapter 20. Cyclotomy and geometric constructions
Chapter 21. Finite fields
Chapter 22. Roots, radicals, and real numbers
Chapter 23. Norms, traces, and discriminants
Chapter 24. Transcendental extensions
Chapter 25. the Artin-Schreier theorem
Chapter 26. Ideal theory
Chapter 27. Noetherian rings
Chapter 28. Integrality
Chapter 29. Dedekind domains
Chapter 30. Algebraic sets and the Nullstellensatz

Produkt-Details

• Erscheinungsdatum: 25.09.2025
• Reihe/Serie: Graduate Studies in Mathematics
• Verlagsort: Providence
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• ISBN-10: 1-4704-8450-1 / 1470484501
• ISBN-13: 978-1-4704-8450-7 / 9781470484507
• Zustand: Neuware